On the Convergence of Smoothed Functional Stochastic Optimization Algorithms*

Smoothed functional gradient algorithm with perturbations distributed according to the Gaussian distribution is considered for stochastic optimization problem with additive noise. A stochastic approximation algorithm with expanding truncations that uses either one-sided or two-sided gradient estimate is given. At each iteration of the algorithm only two observations are required. The algorithm is shown to be convergent under only some mild conditions